"Wiki of the Day" - Newcombs Paradox question

Logic Level 3

If the payoff for Newcomb's problem is as listed in wiki, if the probability of Omega guessing correctly is p at which the expected payoff for choosing only box A is equal to the expected payoff for choosing both boxes , then enter ⌊ 10 ⁶ p ⌋ \left \lfloor 10⁶p \right \rfloor as your answer

Note:

  • I am changing rules slightly in case of only when omega predicts correctly , then if you choose only Box A, then he will give half the amount, and if you choose both boxes then he will give double the amount.


The answer is 667778.

Omek K by Omek K , 15, India

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1 solution

Omek K
Mar 26, 2021

Given

  • 0.5 × 10 ⁶ p 2 × 10 ³ p + ( 10 ⁶ + 10 ³ ) ( 1 − p ) \frac{0.5×10⁶p}{2×10³p+(10⁶+10³)(1-p)} = 1
  • 0.5×10⁶p= (10⁶+10³) -(10⁶-10³)p
  • (1.5×10⁶-10³)p = (10⁶-10³)
  • Therefore p = 10 ⁶ − 10 ³ 1.5 × 10 ⁶ − 10 ³ \frac{10⁶-10³}{1.5×10⁶-10³} = 0.667778...

Therefore required answer is 667778

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